scholarly journals Ought a Four-Dimensionalist To Believe in Temporal Parts?

2009 ◽  
Vol 39 (4) ◽  
pp. 619-646 ◽  
Author(s):  
Kristie Miller
Keyword(s):  
Space Time ◽  
Three Dimensions ◽  
Four Dimensions ◽  
Temporal Parts ◽  
Four Dimensionalism

I borrow the title of this paper, slightly amended, from Parsons’ recent ‘Must a Four-Dimensionalist Believe in Temporal Parts?’ Four-dimensionalism, as I use the term, is the view that persisting objects have four dimensions: they are four-dimensional ‘worms’ in space-time. This view is contrasted with three-dimensionalism, the view that persisting objects have three-dimensions and are wholly present at each moment at which they exist. The most common version of four-dimensionalism is perdurantism, according to which these four-dimensional objects are segmented into temporal parts — shorter lived objects that compose the four-dimensional whole in just the same way that the segments of real earth worms compose the whole worm.

On Stages, Worms, and Relativity

2002 ◽  
Vol 50 ◽  
pp. 223-252 ◽  
Author(s):  
Yuri Balashov
Keyword(s):  
Special Relativity ◽  
Space Time ◽  
Stage Theory ◽  
Temporal Parts ◽  
Spatio Temporal ◽  
Four Dimensionalism

AbstractFour–dimensionalism, or perdurantism, the view that temporally extended objects persist through time by having (spatio-)temporal parts or stages, includes two varieties, the worm theory and the stage theory. According to the worm theory, perduring objects are four–dimensional wholes occupying determinate regions of space–time and having temporal parts, or stages, each of them confined to a particular time. The stage theorist, however, claims, not that perduring objects have stages, but that the fundamental entities of the perdurantist ontology are stages. I argue that considerations of special relativity favor the worm theory over the stage theory.

scholarly journals LARGE QUANTUM GRAVITY EFFECTS: CYLINDRICAL WAVES IN FOUR DIMENSIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 669-686 ◽  
Author(s):  
MARÍA E. ANGULO ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Quantum Gravity ◽  
Symmetry Axis ◽  
Point Of View ◽  
Three Dimensions ◽  
Asymptotic Region ◽  
Four Dimensions ◽  
Cylindrical Waves ◽  
Significant Difference ◽  
Gravity Effects ◽  
Linearly Polarized

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein–Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein–Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein–Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.

On Five Lines, in Space of Four Dimensions, which lie upon a, Quadric Threefold and the Normal Quartic Curves of which they are Chords

1924 ◽  
Vol 22 (2) ◽  
pp. 189-199
Author(s):  
F. Bath
Keyword(s):  
Three Dimensions ◽  
Apparent Contradiction ◽  
Four Dimensions ◽  
Quartic Curve ◽  
Lines In Space ◽  
Quadric Threefold ◽  
Quartic Curves

The connexion between the conditions for five lines of S4(i) to lie upon a quadric threefold,and (ii) to be chords of a normal quartic curve,leads to an apparent contradiction. This difficulty is explained in the first paragraph below and, subsequently, two investigations are given of which the first uses, mainly, properties of space of three dimensions.

scholarly journals Nervous Activity of the Brain in Five Dimensions

Biophysica ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 38-47
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
Norbert Jausovec ◽  
Arjuna P. H. Don ◽  
Sheela Ramanna ◽  
...  
Keyword(s):  
Fourier Analysis ◽  
Nervous Activity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Sets ◽  
Spatial And Temporal Patterns ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Scale Free ◽  
The Brain

The nervous activity of the brain takes place in higher-dimensional functional spaces. It has been proposed that the brain might be equipped with phase spaces characterized by four spatial dimensions plus time, instead of the classical three plus time. This suggests that global visualization methods for exploiting four-dimensional maps of three-dimensional experimental data sets might be used in neuroscience. We asked whether it is feasible to describe the four-dimensional trajectories (plus time) of two-dimensional (plus time) electroencephalographic traces (EEG). We made use of quaternion orthographic projections to map to the surface of four-dimensional hyperspheres EEG signal patches treated with Fourier analysis. Once achieved the proper quaternion maps, we show that this multi-dimensional procedure brings undoubted benefits. The treatment of EEG traces with Fourier analysis allows the investigation the scale-free activity of the brain in terms of trajectories on hyperspheres and quaternionic networks. Repetitive spatial and temporal patterns undetectable in three dimensions (plus time) are easily enlightened in four dimensions (plus time). Further, a quaternionic approach makes it feasible to identify spatially far apart and temporally distant periodic trajectories with the same features, such as, e.g., the same oscillatory frequency or amplitude. This leads to an incisive operational assessment of global or broken symmetries, domains of attraction inside three-dimensional projections and matching descriptions between the apparently random paths hidden in the very structure of nervous fractal signals.

scholarly journals A Survey on the Computation of Quaternions From Rotation Matrices

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Soheil Sarabandi ◽  
Federico Thomas
Keyword(s):  
Three Dimensional ◽  
Rotation Matrix ◽  
Three Dimensions ◽  
Attitude Dynamics ◽  
Euler Parameters ◽  
Four Dimensions ◽  
Rotation Matrices ◽  
Spacecraft Attitude Dynamics ◽  
Applied Fields ◽  
Quaternion Representation

The parameterization of rotations is a central topic in many theoretical and applied fields such as rigid body mechanics, multibody dynamics, robotics, spacecraft attitude dynamics, navigation, three-dimensional image processing, and computer graphics. Nowadays, the main alternative to the use of rotation matrices, to represent rotations in ℝ3, is the use of Euler parameters arranged in quaternion form. Whereas the passage from a set of Euler parameters to the corresponding rotation matrix is unique and straightforward, the passage from a rotation matrix to its corresponding Euler parameters has been revealed to be somewhat tricky if numerical aspects are considered. Since the map from quaternions to 3 × 3 rotation matrices is a 2-to-1 covering map, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clarified. This paper reviews the most representative methods available in the literature, including a comparative analysis of their computational costs and error performances. The presented analysis leads to the conclusion that Cayley's factorization, a little-known method used to compute the double quaternion representation of rotations in four dimensions from 4 × 4 rotation matrices, is the most robust method when particularized to three dimensions.

scholarly journals How Kindergarten Teachers Assess Their Own Professional Competencies

2021 ◽  
Vol 11 (12) ◽  
pp. 769
Author(s):  
Eva Pupíková ◽  
Dalibor Gonda ◽  
Kitti Páleníková ◽  
Janka Medová ◽  
Dana Kolárová ◽  
...  
Keyword(s):  
Classroom Management ◽  
Content Knowledge ◽  
Educational Needs ◽  
Kindergarten Teachers ◽  
Further Education ◽  
Three Dimensions ◽  
Self Assessment ◽  
Teaching Competencies ◽  
Four Dimensions

One of the requirements of Education 4.0 is that students and practitioners should be involved in the creation of the content of study plans. Therefore, in the present research we focused on identifying the further educational needs of kindergarten teachers. Teachers’ educational needs were divided into four dimensions: ‘content knowledge’, ‘diagnostic knowledge’, ‘didactical knowledge’, and ‘classroom management knowledge’. In parallel, we discovered how teachers assess the level of their own teaching competencies. Based on the obtained data, we identified that teachers have the greatest need for further education in the dimension of ‘diagnostic knowledge’ and that the need for their further education in this dimension did not depend on the length of practice. In the other three dimensions, a declining trend in teachers’ educational needs has been recorded with an increasing length of practice, declining significantly in three of the four dimensions examined. The study points to the need to create in-service courses for kindergarten teachers to deepen their ‘diagnostic knowledge’ and thus ensure the sustainability of the quality of pre-school education for children. Teachers‘ self-assessment of their own teaching competencies corresponds to their educational needs, which supports the relevance of the findings on the further educational needs of kindergarten teachers. This study aimed to obtain relevant data on which the improvement of the higher education of future kindergarten teachers might be based. At the same time, this would allow the analysis and tailoring of the content of professional development courses to the needs of in-service kindergarten teachers.

scholarly journals Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3

2017 ◽  
Vol 3 ◽  
pp. e123 ◽  
Author(s):  
Ken Arroyo Ohori ◽  
Hugo Ledoux ◽  
Jantien Stoter
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Three Dimensions ◽  
Time And Space ◽  
3D Objects ◽  
Levels Of Detail ◽  
Higher Dimensional Space Time ◽  
Space Scale ◽  
Higher Dimensional ◽  
Dimensional Space Time

Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (S3) followed by a stereographic projection to ℝ3, which results in an inwards-outwards fourth axis. Our focus is in using these projections from ℝ4to ℝ3, but they are formulated from ℝnto ℝn−1so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

The quantum consistency of the 12-dimensional theory

2016 ◽  
Vol 31 (04n05) ◽  
pp. 1650010
Author(s):  
Simon Davis
Keyword(s):  
Cosmological Constant ◽  
Moduli Space ◽  
Dimensional Reduction ◽  
Text Structure ◽  
Three Dimensions ◽  
Supersymmetric Theory ◽  
Particle Spectrum ◽  
Dimensional Theory ◽  
Cosmological Constant Problem ◽  
Four Dimensions

By considering the 12-dimensional superalgebra, inferences are drawn about the finiteness of the 12-dimensional theory unifying the superstring models. The dimensional reduction of the nonsupersymmetric theory in four dimensions to a supersymmetric action in three dimensions is established for the bosonic sector. It is found to be the quotient by [Formula: see text] of the integration over the fiber coordinate of a theory with [Formula: see text] supersymmetry. Consequently, a flow on the moduli space of Spin(7) manifolds from a [Formula: see text] structure with [Formula: see text] supersymmetry yielding a phenomelogically realistic particle spectrum to a [Formula: see text] holonomy manifold compatible with supersymmetry in three dimensions and a nonsupersymmetric action in four dimensions, solving the quantum cosmological constant problem, is proven to exist. The projection of the representations of the [Formula: see text] superalgebra of the 12-dimensional theory to four dimensions include nonperturbative string solitons that are more stable because the dynamics is described by supersymmetric theory with a higher degree of finiteness.

How do people judge fairness in supervisor and peer relationships? Another assessment of the dimensions of justice

2019 ◽  
Vol 73 (12) ◽  
pp. 1632-1663 ◽  
Author(s):  
Marion Fortin ◽  
Russell Cropanzano ◽  
Natàlia Cugueró-Escofet ◽  
Thierry Nadisic ◽  
Hunter Van Wagoner
Keyword(s):  
Factor Analysis ◽  
Organizational Justice ◽  
Peer Relationships ◽  
Three Dimensions ◽  
Informational Justice ◽  
Justice Research ◽  
Four Dimensions ◽  
Follow Up Studies ◽  
Theoretical Considerations

The ultimate goal of organizational justice research is to help create fairer workplaces. This goal may have been slowed by an inattention to the criteria that workers themselves use to ascertain what they believe is fair. Referred to as ‘justice rules’, these were originally determined by theoretical considerations and organized in four dimensions (distributive, procedural, interpersonal and informational justice). There have been few attempts to investigate how far these classical norms represent fairness experiences and concerns in modern workplaces, especially in the context of working with peers. In a person-centric study, we investigate which rules people use when judging the fairness of interactions with supervisors and peers. This allows us to identify 14 new justice rules that are not taken into account by traditional measures. When subjected to factor analysis in follow-up studies, the enlarged set of rules suggests a more parsimonious structure for organizational justice, with only three dimensions apiece for supervisor and peer justice. We term these factors relationship, task, and distributive justice. Furthermore, we find that the resulting model of justice rules is a good predictor of attitudes in relation to supervisors and peers and can provide additional insights into how to understand and manage justice.

scholarly journals Klein Gordon Field in FLRW Space-Time

2020 ◽  
Vol 13 (13) ◽  
pp. 1-4
Author(s):  
S.K. Sharma ◽  
P.R. Dhungel ◽  
U. Khanal
Keyword(s):  
Spherical Harmonics ◽  
Energy Momentum Tensor ◽  
Equation Of Motion ◽  
Momentum Tensor ◽  
Space Time ◽  
Wkb Approximation ◽  
Temporal Parts ◽  
Klein Gordon ◽  
Current Energy ◽  
Particle Current

As a continuation of solving the equations governing the perturbation of the Friedmann-Lemaitre-Robertson- Walker (FLRW) space-time in Newman-Penrose formalism, the behaviour of the massive Klein-Gordon (KG) field coupled to the FLRW has been investigated. The Equation of Motion has been written and solved separately for radial and temporal parts. The former solution has come to be in terms of the Gegenbauer polynomials and spherical harmonics and the latter being in the WKB approximation. The particle current, energy momentum tensor and potential have also been obtained.

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